Chapter 1
1-1
Chapter Goals
After completing this chapter, you should be
able to:
„
„
♦Population vs. Sample
Chapter 1
Introduction and Data Collection
♦Discrete vs. Continuous data
„
Chap 1-1
Explain the difference between descriptive and
inferential statistics
Describe the difference between inductive and deductive
reasoning
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Chap 1-2
What is Statistics?
„
Why study statistics?
What Is Statistics?
„
„
To become a better decision maker
Statistics involves
Statistics is a tool used to gather, present,
analyze, and interpret data for decision
making
collecting,
organizing,
summarizing, and
analyzing data
„
♦Primary vs. Secondary data types
♦Categorical vs. Numerical data ♦Time Series vs. Cross-Sectional data
„
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Describe key data collection and sampling methods
Know key definitions:
and using the results for decision making
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Chap 1-3
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Chap 1-4
Why Study Statistics?
Why Study Statistics?
(continued)
(continued)
„
„
Business decision making:
„
Personal decision making:
„
everyone can benefit from the ability to make informed
decisions
managers in all business fields must make
choices based on statistical evidence
Examples:
„
Examples:
smoking and health
recalls and car safety
marital status or sex or age vs. car insurance rates
passing offense and points scored
etc....
marketing surveys,
accounting audits,
economics forecasts,
manufacturing quality control,
finance trends
„
Many everyday events and decisions involve
statistical reasoning and analysis of data
„
Recent news report: night lights and nearsightedness
„ see file nightlight_news.htm
Click here to see news article
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Chap 1-5
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Chap 1-6
Chapter 1
1-2
Two broad categories of constraints:
Key Aspects of Decision Making
„
Objectives
„
„
Alternatives
Without alternatives, no choices are necessary. These
define the alternative means of satisfying the
objective
„
Environmental:
„
These represent the goals of the decision maker - they
define the problem and determine the incentives of
the decision maker
„
Constraints
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Informational:
„
Constraints determine the boundaries of the feasible (or
allowable) set of actions by the decision maker
Chap 1-7
factors that cannot be controlled by the decision
maker
Physical
(resources, budget)
Technical
(technology)
Legal
(government barriers or restrictions)
Behavioral
(customs or traditions)
results of alternative actions are uncertain
Risk
Uncertainty
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Chap 1-8
Completing the
Decision Making Process
Establish objectives
Define the problem
„
„
„
Decision
Process
Flowchart
Data collection and analysis
Information is needed to support the decision
making process
Decision
„
Consider input and
resource constraints
Identify types and
availability of existing
data
Use graphical summary
techniques
An action is chosen based on objectives,
alternatives, constraints, and data
Scope of this
course:
Identify possible
solutions
Consider sources of
variation
Gather data
Summarize, analyze,
and interpret data
Select the best
expected solution
Consider legal and other
constraints
Develop surveys or
sampling plans to
acquire needed data
Use numerical summary
techniques and analytical
methods
Evaluate risk and
uncertainty
Implement the
decision
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Chap 1-9
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Deductive reasoning
Statistical Reasoning
„
Chap 1-10
(from general to specific)
Statistics is more than mathematical
manipulation, it is a way of thinking about
data
Example
„
All children are short
(Major premise = general statement)
„
Statistical logic:
We use Inductive Logic rather than Deductive
Logic
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Chap 1-11
„
Tom is a child (Minor premise = specific example)
„
Therefore . . .
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Chap 1-12
Chapter 1
1-3
Deductive reasoning
(from general to specific)
Using Venn diagrams:
(continued)
Example
„
„
“Children” represents an entire group (the
“population”) about which a characteristic is
known
„
“Tom” is one of the group
(a “sample observation” or
“member” of the population)
All children are short
(Major premise = general statement)
„
Tom is a child (Minor premise = specific example)
„
Therefore Tom is short (conclusion)
„
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Chap 1-13
Tom
and so Tom has the group characteristic
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Inductive reasoning
Chap 1-14
Inductive reasoning
(from specific cases to the general case)
(from specific cases to the general case)
(continued)
Example
Example
„
I have seen many children
„
I have seen many children
„
All of them were short
„
All of them were short
„
Therefore . . .
„
Therefore, the average height of
children is likely to be small
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Chap 1-15
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Using Venn diagrams
„
Chap 1-16
Tools of Business Statistics
„
An observed characteristic of a sample
of children leads us to infer a
characteristic of the entire population
(even though they all have not been
observed)
Descriptive statistics
„
„
„
Children I
have seen
Chap 1-17
Collecting, presenting, and describing data
Inferential statistics
All Children
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Children
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Drawing conclusions and/or making decisions
concerning a population based only on
sample data
Chap 1-18
Chapter 1
1-4
Descriptive Statistics
„
Data Sources
Collect data
„
e.g. Survey, Observation,
Primary
Secondary
Data Collection
Data Compilation
Experiments
Print or Electronic
„
Present data
„
„
Characterize data
„
Observation
e.g. Charts and graphs
e.g. Sample mean =
∑x
Experimentation
i
n
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Chap 1-19
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Populations and Samples
„
„
Examples:
Population
a b
All likely voters in the next election
All parts produced today
All sales receipts for November
Examples:
x y
Chap 1-21
Sample data is needed to make inferences
about population parameters
„
„
c
gi
o
z
n
r
u
y
Chap 1-22
Why Sample?
Why Gather Data?
„
b
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Data Collection and Sampling
„
cd
o p q rs t u v w
1000 voters selected at random for interview
A few parts selected for destructive testing
Every 100th receipt selected for audit
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Sample
ef gh i jk l m n
A Sample is a subset of the population
„
Chap 1-20
Population vs. Sample
A Population is the set of all items or individuals
of interest
„
Survey
i.e., the true proportion of defective parts in large shipment
the true mean of a population
„
Less time consuming than a census
„
Less costly to administer than a census
„
It is possible to obtain statistical results of a
sufficiently high precision based on samples
To reach valid inferences, we need to examine a
representative sample of the population
„
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the observed sample characteristic is used to infer the likely
value of the population characteristic.
Chap 1-23
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Chap 1-24
Chapter 1
1-5
Sampling Techniques
Statistical Sampling
„
Samples
Non-Probability
Samples
Judgement
Items of the sample are chosen based on
known or calculable probabilities
Probability Samples
Probability Samples
Simple
Random
Convenience
Systematic
Stratified
Simple
Cluster
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Chap 1-25
Systematic
Cluster
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Chap 1-26
Simple Random Samples
Example
„
Every individual or item from the population has
an equal chance of being selected
„
Selection may be with replacement or without
replacement
„
Samples can be obtained from a table of
random numbers or computer random number
generators
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Stratified
Random
Chap 1-27
„
Suppose the output from a production
process is identified by a code number
„
For simplicity assume that the code number
runs from 1 to 10,000 (hence the population
consists of 10,000 objects)
„
A random sample of 100 items could be
drawn by using a random number generator
to create 100 numbers corresponding to
100 codes in the population
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Example
Chap 1-28
Stratified Samples
(continued)
„
If we require that each of the randomly generated
numbers be unique then this technique represents
sampling without replacement
„
Sampling with replacement would allow for the
possibility that a particular item be selected more
than once
„
This has the advantage of ensuring that the probability of
selecting an object remains constant and independent
across trials. The obvious disadvantage is the potential for
redundant observations
„
Population divided into subgroups (called strata)
according to some common characteristic
„
Simple random sample selected from each
subgroup
„
Samples from subgroups are combined into one
Population
Divided
into 4
strata
Sample
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Chap 1-29
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Chap 1-30
Chapter 1
1-6
Stratified Random Sampling
Systematic Samples
(continued)
„
Decide on sample size: n
„
The separate samples from the different
strata do not need to be the same size
„
Divide frame of N individuals into groups of k
individuals: k=N/n
„
the total sample could be drawn so that the
proportion from each strata reflects the
composition of the population
„
Randomly select one individual from the 1st
group
„
Select every kth individual thereafter
N = 64
n=8
First Group
k=8
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Chap 1-31
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Chap 1-32
Systematic Sampling Example
Cluster Samples
„
A sample can be gathered by choosing items
according to a set rule
„
Example
„
„
Population is divided into several “clusters,”
each representative of the population
„
A simple random sample of clusters is selected
„
If the objects in a population of 1,000 are randomly
ordered then a sample of size 100 could be chosen
by selecting every tenth item
All items in the selected clusters can be used, or items can be
chosen from a cluster using another probability sampling
technique
Population
divided into
16 clusters.
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Chap 1-33
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Validity of Results
Chap 1-34
A Potential Problem: Sampling Error
„
The validity of the sample results depends on
how the sample is gathered
„
There is no “best” technique for gathering a
sample
„
The user must decide which sampling
technique best suits the current problem
„
Given that a sample is to be taken, there are
two sources of error that can result.
„
1. sampling error
we will not know the true population parameters exactly
because we are using only a subset of the population
„
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Randomly selected
clusters for sample
2. nonsampling error
error due to other factors (arises independently of the
sampling technique involved)
Chap 1-35
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Chap 1-36
Chapter 1
1-7
Example
Random Sampling
„
Suppose young male survey workers only
approach attractive females to complete a survey
„
Then sample results may be biased since all
members of the population did not have an equal
chance to be selected for the sample. Young
females may not represent the relevant
population
„
Notice that the word “random” was used in
each example above to describe the method
of selecting elements from a population for a
sample
„
Only random sampling plans generate
information that reliably mirrors the extent
and pattern of the variation in the population
The results would be biased due to nonsampling
error.
„
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Chap 1-37
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Chap 1-38
Sampling Bias
Random Sampling
(continued)
„
Simply put, a sample is random if each
element of the population is equally likely to
be selected for the sample
„
„
„
Naturally, the actual elements selected for the sample are
variable, and some unusual sample results may occur
„
This variability in sample results leads to variability in
estimating population parameters . . .
„
but the random nature of the sample insures that the
results can be statistically investigated for insight into their
reliability
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Non-random sampling plans may introduce
biases. Bias destroys the ability to make good
decisions.
Examples of sampling plans that may generate
biases are:
„
„
Chap 1-39
„
„
a. Sampling from the same location in all containers
or bins.
b. Sampling every nth item from a production run if
production variation is not random.
c. Ignoring lot portions that are inconvenient to sample.
d. Sampling performance at constant (specified) time
intervals.
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Chap 1-40
Key Definitions
„
A population is the entire collection of things
under consideration
„
„
Data Types
Data
A parameter is a summary measure computed to
describe a characteristic of the population
Attribute
(Categorical)
A sample is a portion of the population
selected for analysis
„
Variable
(Numerical)
Examples:
„
„
A statistic is a summary measure computed to
describe a characteristic of the sample
„
„
Marital Status
Political Party
Satisfactory vs. Defective
Eye Color
(Defined categories)
Discrete
Examples:
„
„
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Chap 1-41
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Number of Children
Defects per hour
(Counted items)
Continuous
Examples:
„
„
Weight
Voltage
(Measured
characteristics)
Chap 1-42
Chapter 1
1-8
Attribute Data
„
„
„
Variable Data
categories can be identified
not measured in physical units
Examples:
„
„
„
scratched vs. scratch-free
spreads peanut butter first vs. spreads jelly first
satisfactory vs. defective
any “yes” vs. “no” question
cars are “4 cylinder”, “6 cyl”, “8 cyl”, or “other”
marital status categories ...
„
„
„
„
„
„
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Chap 1-43
expressed in actual physical units
can be measured or given a numerical value
Examples:
Continuous
„ Voltage
„ Time
„ Weight
„ Income
„ Hardness
Discrete
„
Number of brothers and sisters
„
Number of data entries per hour
„
Number of absences per month
„
Number of change orders per week
„
Number of rings before phone is
answered
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Chap 1-44
Data Types
Data Types
(continued)
„
„
„
Sales (in $1000’s)
Time Series Data
Ordered data values observed over time
Cross Section Data
„
Data values observed at a fixed point in time
2003
2004
2005
2006
Atlanta
435
460
475
490
Boston
320
345
375
395
Cleveland
405
390
410
395
Denver
260
270
285
280
Time
Series
Data
Cross Section
Data
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Chap 1-45
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Inferential Statistics
„
Inferential Statistics
Drawing conclusions and/or making decisions
concerning a population based on sample results.
Making statements about a population by
examining sample results
„
Sample statistics
(known)
Population parameters
Inference
Estimation
„
(unknown, but can
be estimated from
sample evidence)
„
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Population
Chap 1-47
e.g.: Estimate the population mean
weight using the sample mean
weight
Hypothesis Testing
„
Sample
Chap 1-46
e.g.: Use sample evidence to test
the claim that the population mean
weight is 120 pounds
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Chap 1-48
Chapter 1
1-9
Description vs. Inference
Description vs. Inference
2. Inference
1. Description
„
a. graphical techniques for summarizing and
presenting information
Examples: graphs, charts, histograms,
other visual displays – text chapter 2
„
„
What can be said from sample data?
„
At what levels of confidence?
„
With what sources and amount of error?
b. numerical summary values
Examples: mean, median, standard deviation,
quartiles – text chapter 3
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Chap 1-49
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Chap 1-50
Road Map
Semester Road Map
„
A useful summary chart (text p. 7)
„
It might be helpful to think of the
course material in 3 main blocks
„
(see next slide)
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Chap 1-51
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Chap 1-52
Survey Design Steps
Survey Design Steps
(continued)
„
Define the issue
„
what are the purpose and objectives of the survey?
„
Define the population of interest
„
Formulate survey questions
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„
„
make questions clear and unambiguous
„
use universally-accepted definitions
„
limit the number of questions
Chap 1-53
Pre-test the survey
„
pilot test with a small group of participants
„
assess clarity and length
„
Determine the sample size and sampling
method
„
Select Sample and administer the survey
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Chap 1-54
Chapter 1
1-10
Types of Questions
Data from Surveys
Closed-end Questions
„
„
„
Select from a short list of defined choices
Example: Major: __business __liberal arts
__science __other
Open-end Questions
„
„
Respondents are free to respond with any value, words, or
statement
Potential problems with surveys
„
What population is being sampled?
„
Are responses random and representative?
„
Are questions likely to generate truthful and
relevant data?
„
How confident are we that survey responses
accurately represent the population?
Example: What did you like best about this course?
Demographic Questions
„
„
Questions about the respondents’ personal characteristics
Example: Gender: __Female __ Male
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Chap 1-55
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Chap 1-56
Survey Errors
Survey Errors
(continued)
„
1. Coverage error or selection bias . . .
„
„
„
„
may occur if selected members of the population are not
represented in the survey sample
2. Nonresponse error or nonresponse bias . . .
„
3. Sampling error . . .
„
may occur if those who respond are not representative of the full
population. This is why survey follow-ups are done to try to get a
large response rate.
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will always exist, since only a sample is obtained from the
population. Statistical methods can be used to report the size
of this error.
4. Measurement Error . . .
„
may exist if the questions (or the interviewer’s non-verbal
actions) influence responses. Non-neutral wording can elicit
emotional reactions that may not appear if questions are
worded differently.
Chap 1-57
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Chap 1-58
Chap 1-59
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Chap 1-60
It’s A Magical World
Bill Watterson
Scholastic, Inc., 1996
Yandell - GSBA 502
Chapter 1
1-11
Link to Survey and Polling Sites
„
Visit the links collected on this web page to find
out more about survey and polling techniques,
or to see what recent opinion polls reveal about
current social, political, and economic issues:
links to national polling and opinion survey sites
Yandell - GSBA 502
Chap 1-61
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Chap 1-62
Class Discussions Questions
Discussion Question 2
1. A newspaper clipping appeared stating
„
„
“A random inspection of 4500 tires removed from cars
in four American cities showed that 1125 were worn
down below tread indicators, Firestone [tire company]
reports. The tire company said this is a potentially
dangerous practice because 90 percent of tire trouble
occurs in the 10 percent of tread life.”
2. In the late 1960s and early 1970s metal-studded
snow tires were widely used during winter months
in Canada and the northern U.S. to increase
traction on icy roads. The studs were blamed for
tearing up roads and were ultimately banned in
many states. A newspaper article reported that . . .
“National Safety Council tests have demonstrated that
studs improve stopping distance by as much as 50 percent
and best starting traction in some instances as high as 50
percent on ‘glaze ice’ near the freezing point – soft ice that
is easy for the studs to grip.”
Do the statistics and information presented
mislead or illuminate the issue of tire safety?
„
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Chap 1-63
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Chap 1-64
Discussion Question 2
Discussion Question 3
(continued)
„
Nevertheless, according to the article, a survey in
Ontario, Canada . . .
„
Are statistical procedures a
replacement for intuition and
common sense?
„
Is the reverse true?
„
What should be done if the
conclusions from a statistical
analysis seem to conflict with
intuition and common sense?
“concluded that vehicles with studded tires are involved
in a somewhat bigger percentage of accidents on icy
roads than those on clear surfaces.”
„
Give possible explanations for the higher
accident rates for drivers with studded snow tires
on icy roads.
Can you think of flaws in the design of the Ontario
study, or in the description of the findings, the drawing
of inferences, or the (implied) decision of the study?
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Chap 1-65
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Chap 1-66
Chapter 1
1-12
For further reading:
„
Chapter Summary
“How numbers are tricking you”
„
Reviewed key data collection methods
„
Introduced key definitions:
By Arnold Barnett
Technology Review, October 1994
Click here to see article
Yandell - GSBA 502
Chap 1-67
♦Population vs. Sample
♦Primary vs. Secondary data types
♦Attribute vs. Variable data
♦Time Series vs. Cross-Sectional data
„
Examined descriptive vs. inferential statistics
„
Described different sampling techniques
„
Reviewed types of data
Yandell - GSBA 502
Chap 1-68